Exponentially Fitted Modified Upwind Scheme For Singularly Perturbed Convection-Diffusion Problem

Abstract

In this thesis, an exponentially fitted modified upwind difference scheme is presented for solving singularly perturbed convection-diffusion two point boundary value problems whose solution exhibits right boundary layer. A fitting factor is introduced in a modified upwind scheme and is obtained from the theory of singular perturbations. Then, fitted modified upwind scheme is developed and a three term recurrence relation is obtained. A tri-diagonal finite difference scheme is obtained and is solved by using the Thomas algorithm. To validate the applicability of the proposed method two model examples have been considered and solved for different values of perturbation parameters ε and mesh size h. Both theoretical stability and numerical first order of convergence have been established for the method. The numerical results have been presented in tables, graphs and further to examine the effect of fitted parameter on right boundary layer of the solution and oscillatory behavior of the solution. Several linear and nonlinear problems are solved and observed, which show the presented method approximates the exact solutions very well. Concisely,